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arXiv:hep-th/0112163 · Journal of Mathematical Physics

On integrable Hamiltonians for higher spin XXZ chain

Andrei G. Bytsko

Published Aug 21, 2003• 27 citations
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Abstract

Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to 32 are given. Relations between Hamiltonians for some Uq(sl2)-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable Uq(sl2)-symmetric Hamiltonian for an open chain.

DOI
10.1063/1.1591054

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Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to 32 are given. Relations between Hamiltonians for some Uq(sl2)-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable Uq(sl2)-symmetric Hamiltonian for an open chain.
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Rational QQQ-systems for integrable spin chains without U(1)U(1)U(1) symmetry
The Q Q -system is an efficient method for finding complete physical solutions of Bethe Ansatz equations, but so far its application has been confined to systems possessing U(1) U ( 1 ) symmetry. We extend the rational Q Q -system framework to integrable spin chains without U(1) U ( 1 ) symmetry, exemplified by the closed XXZ model with anti-diagonal twists and the open XXZ model with non-diagonal boundary fields. We demonstrate that the Q Q -system can be derived by combining TQ T Q -relation with fusion relations of higher-spin transfer matrices. This yields QQ Q Q -relations analogous to the U(1) U ( 1 ) symmetric case but incorporating additional inhomogeneous terms. We present numerical solutions that are validated against exact diagonalization, confirming that it generates all and exclusively physical solutions.